Re: Are open formulae really needed?

From: Torkel Franzen (torkel_at_sm.luth.se)
Date: 01/30/05 

Date: 30 Jan 2005 09:42:41 +0100

"LordBeotian" <pokipsy76@CANCELLAMIyahoo.it> writes:

> Uhm... I would hope in this case that M-wff canot be theorems.

  Why not? You get the M-wffs by adding a lot of constants to the
language, and so for example a=a will be such a theorem. Shoenfield
does the semantics of first order logic this way.

> What I find a bit disturbing is the possibility that an open formula can
> came up as a theorem of FOL.

  There are formalizations of the rules of first order logic in which
only closed sentences are theorems. For example, the one given by
Quine, with modus ponens as the only rule of inference, and only
closed axioms.